Hw28 - Overton Mays Homework 28 Due 4:00 am Inst Turner This print-out should have 12 questions Multiple-choice questions may continue on the next

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Overton, Mays – Homework 28 – Due: Apr 13 2005, 4:00 am – Inst: Turner 1 This print-out should have 12 questions. Multiple-choice questions may continue on the next column or page – fnd all choices beFore answering. The due time is Central time. 001 (part 1 oF 2) 10 points A moon oF a planet like the Earth is 579000 km distant From the planet’s center, and it com- pletes an orbit in 35 . 4 days. Determine the moon’s orbital speed. Correct answer: 1189 . 44 m / s. Explanation: Using the obvious Formula v T = 2 π R , we obtain For the moon’s orbital speed v = 2 π R T = 2 π (579000 km ) 35 . 4 days = 1189 . 44 m / s . 002 (part 2 oF 2) 10 points How Far does the moon ”Fall” toward the planet in 1 . 29 s? Correct answer: 2 . 03308 mm. Explanation: The centripetal acceleration a oF the motion oF the moon is a = v 2 R = (1189 . 44 m / s ) 2 5 . 79 × 10 8 m = 0 . 00244345 m / s 2 . Hence, in time t the moon Falls a distance d = 1 2 a t 2 = 1 2 (0 . 00244345 m / s 2 ) (1 . 29 s ) 2 = 0 . 00203308 m = 2 . 03308 mm . 003 (part 1 oF 1) 10 points A cylindrical habitat in space 7 . 35 km in di- ameter and 31 . 7 km long has been proposed (by G.K. O’Neill, 1974). Such a habitat would have cities, land, and lakes on the inside sur- Face and air and clouds in the center. This would all be held in place by rotation oF the cylinder about its long axis. The acceleration oF gravity is 9 . 8 m / s 2 . How Fast would the cylinder have to rotate to imitate the Earth’s gravitational feld at the walls oF the cylinder? Correct answer: 0 . 0516398 rad / s. Explanation: The radius oF a cylinder with d = 7 . 35 km is r = d 2 = 7 . 35 km · 1000 m 1km 2 = 3675 m . To simulate the Earth’s gravitational feld g = 9 . 8 m / s 2 at the walls oF the cylinder the Following relation must hold: g = ω 2 r = v 2 r . ThereFore the angular speed ω oF the cylinder has to be ω = r g r = r 9 . 8 m / s 2 3675 m = 0 . 0516398 rad / s . 004 (part 1 oF 1) 10 points Two satellites A and B orbit the same planet. Both satellites have circular orbits oF respec- tive radia r A and r B = 2 r A . The masses oF the two satellites are respectively m A and m B = 3 m A . A B
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Overton, Mays – Homework 28 – Due: Apr 13 2005, 4:00 am – Inst: Turner 2 What is the ratio of the orbital speeds of the two satellites? 1.
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This note was uploaded on 03/22/2008 for the course PHY 303K taught by Professor Turner during the Spring '08 term at University of Texas at Austin.

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Hw28 - Overton Mays Homework 28 Due 4:00 am Inst Turner This print-out should have 12 questions Multiple-choice questions may continue on the next

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